Magnetic resonance imaging (MRI) methods use the interaction between magnetic field and nuclear spins with the purpose of forming two-dimensional or three-dimensional images. These methods are widely used these days, notably in the field of medical diagnostics. The advantages of the MR methods are that they do not require ionizing radiation and they are usually not invasive. MRI is used for example as imaging technique to visualize structural abnormalities of the body, e.g. tumour development.
An MRI apparatus uses a powerful magnetic field to align the magnetization of some atomic nuclei in the body, and radio frequency fields to systematically modify the alignment of this magnetization. This causes the nuclei to produce a rotating magnetic field detectable by a scanner. This information is recorded to construct an image of the sampled area of the body. Magnetic field gradients cause nuclei at different locations to rotate at different speeds. By using gradients in different directions 2D images or 3D volumes can be obtained in arbitrary orientation.
According to the MR method in general, the body of a patient or in general an object to be examined is arranged in a strong, uniform magnetic field B0 whose direction at the same time defines an axis, normally the z-axis, of the coordinate system on which the measurement is based.
Any temporal variation of the magnetization can be detected by means of receiving RF antennas, which are configured and oriented within an examination volume of the MR device in such a manner that the temporal variation of the magnetization is measured in the direction vertically to the z-axis.
Spatial resolution in the body can be realized by switching magnetic field gradients. They extend along the three main axes and are superposed on the uniform magnetic field, leading to a linear spatial dependency of the spin resonance frequency. The signal picked up in the receiving antennas then comprises components of different frequencies which can be linked to different locations in the body/subject.
The signal data obtained by the receiving antennas matches to the spatial frequency domain and are called k-space data. The k-space data generally include multiple lines acquired with different phase encoding. Each line is digitized by collecting a number of samples. A set of samples of k-space data is transformed to an MR image, e.g. by inverse Fourier transformation.
Furthermore the document “Combined compressed sensing and parallel MRI compared for uniform and random cartesian undersampling of k-space” by D. S. Weller et al. (2011 IEEE Int. Conf. on Acoustics, Speech, and Signal Processing. Prague, Czech Republic, May 2011, pp. 553-6) discloses the combination of compressed sensing and variable density random k-space sampling. Combining both methods enables imaging with greater undersampling than accomplished previously.
United States Published Application US 20090274356 A1 describes a method for generating a magnetic resonance image of a subject. The disclosed invention relates to magnetic resonance imaging using compressed sensing which allows recovery of a sparse signal, or a signal that can be made sparse by transformations, from a highly incomplete set of samples, and thus has the potential for significant reduction in MRI scan time.